Geometry

Solids

Medium

How many meters of cloth 6 metre wide will be required to make a conical tent, the radius of whose base is 21m and height is 20m?

209 metre

627 metre

638 metre

319 metre

✅ Correct Option: 4

The tent is conical in shape and requires cloth to cover the curved surface area (the slanted outer surface, excluding the base).

Given:

Radius of tent base: $r = 21$ m
Height of tent: $h = 20$ m
Width of cloth available $= 6$ m

The slant height is needed since the cloth wraps around the slanted side.

Using Pythagoras theorem:

$l = \sqrt{r^2 + h^2}$

$l = \sqrt{21^2 + 20^2}$

$l = \sqrt{441 + 400}$

$l = \sqrt{841}$

$l = 29$ m

The curved surface area of the cone:

Curved Surface Area $= \pi r l$

$= \frac{22}{7} \times 21 \times 29$

$= 22 \times 3 \times 29$

$= 66 \times 29$

$= 1914$ m²

The cloth comes in a roll that is $6$ m wide. The length of cloth required:

Length $= \frac{\text{Area}}{\text{Width}}$

Length $= \frac{1914}{6}$

Length $= 319$ metres

Therefore, $319$ metres of cloth is required.

2022: 6 Oct Shift 1

If the outer surface area of cylinder is pointed @ Rs 0.5/cm^2, then the total cost of painting is

2026: 18 May Shift 1

Consider the surface areas of the following solids.

(A) A cuboid of 12 cm long, 7 cm broad, and 5 cm high.

(B) A cylinder of radius 3.5 cm and height 60 cm.

(D) A sphere of radius 12.5 cm.

Arrange the above in decreasing order.

2025: 20 May Shift 1

The base radius of a cone is 21 cm and the height is 28cm, then which of the following is/are correct?

(A) Slant height = 35 cm

(B) Slant height = 33 cm

(D) Curved Surface Area = 2310 cm²

Choose the correct answer from the options given below:

2022: 6 Oct Shift 1

If each side of a cube is reduced by 50%, the surface area will reduced by.

2025: 14 May Shift 1

Match the given areas of various solid objects with their respective formulae:

List I	List II
Area of solid object	Formula
(A) Lateral surface area of a cylinder	(I) $\pi r\sqrt{r^2 + h^2}$
(B) Total surface area of a hemisphere	(II) $4\pi r^2$
(C) Lateral surface area of a cone	(III) $2\pi rh$
(D) Surface area of a sphere	(IV) $3\pi r^2$

(Where, r = radius of the solid shape (or base) and h = height of the solid shape.)

Choose the correct answer from the options given below:

2023: 15 June Shift 2

The volume of a sphere of radius r is obtained by multiplying its surface area with:

How many meters of cloth 6 metre wide will be required to make a conical tent, the radius of whose base is 21m and height is 20m?

Solution

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